Those look like crypts to me. They'll spread if you give them enough light and make them happy.
There are certain branches that are long and skinny, one of those might look good. I've discovered that bettas seem to love big old hunks of loose Java moss that they can dive into, and some Java fern should do pretty well. Anubias of some sort might also be nice, if you have a decent amount of light from the room or a window.
There are some pretty nerite snails like the olive, the horned, and the sun-spike nerites, you could add a few of those. They might end up needing algae wafers in place of the algae if it runs out, but I think you'd like a few. Plus, there's almost no way in the world that a betta could hurt them, even if they were actually interested in the snails.